Card Games – Trigonometric Functions
This document includes a collection of card games.
1.
Periodic Functions Cards: Cards depicting various
transformations of y = sinx are provided. Identify the key
properties (amplitude, period, maximum & minimum values) of
each graph and match graphs that share common key
properties.
2.
Key Properties of the Sine Function Cards: Explore the key
properties of y = sin x by matching cards depicting the name of
each key property with a visual image, value or brief description,
and definition. Variations of this game include Memory Match
and Go Fish.
3.
Relations Cards: Classify various graphs and contextual
situations as either linear, quadratic, periodic or other. Determine
whether or not each relation is a function.
Periodic Functions Cards
The card set contains 16 “Graph” cards
The answer key (last page) references the graph card numbers.
The cards can be used in a variety of ways.
Suggestion 1
Pick one of the graph cards. Determine the key properties of the graph.
Suggestion 2
Pick one of the graph cards. Find all cards that have a curve with the same period.
Suggestion 3
Pick one of the graph cards. Find all cards that have a curve with the same maximum value (or minimum
value).
Suggestion 4
Pick one of the graph cards. Find all the cards that have a curve with the same amplitude.
Suggestion 5
Pick one of the graph cards. Sketch a curve with the same amplitude and period but different maximum
and minimum values.
Suggestion 6
Create additional cards for the set.
Graph 1
Graph 2
Graph 3
Graph 4
Graph 5
Graph 6
Graph 7
Graph 8
Graph 9
Graph 10
Graph 11
Graph 12
Graph 13
Graph 14
Graph 15
Graph 16
Key Properties
No.
Maximum Value
Minimum Value
Amplitude
Period
1
1.0
-1.0
1.0
360
2
1.0
-1.0
1.0
90
3
2.0
0.0
1.0
90
4
2.0
0.0
1.0
90
5
3.0
-1.0
2.0
90
6
2.0
-2.0
2.0
90
7
2.0
-2.0
2.0
180
8
0.5
-0.5
0.5
180
9
0.5
-0.5
0.5
120
10
2.0
1.0
0.5
120
11
-0.5
-1.5
0.5
120
12
0.0
-2.0
1.0
120
13
3.0
0.0
1.5
180
14
3.0
0.0
1.5
360
15
3.0
-1.0
2.0
180
16
-0.5
-1.5
0.5
360
Key Property
Graphs with the same key property
1, 2
3, 4, 6, 7, 10
Maximum Value
5, 13, 14, 15
8, 9
11, 16
1, 2, 5, 15
3, 4, 13, 14
Minimum Value
6, 7, 12
8, 9
11, 16
1, 2, 3, 4, 12
Amplitude
5, 6, 7, 15
8, 9, 10, 11, 16
13, 14
1, 14, 16
Period
2, 3, 4, 5, 6
7, 8, 13, 15
9, 10, 11, 12
Key Properties of the Sine Function cards
The set contains 44 cards, four cards for each key property.
Each key property has a card depicting:
• property name
• visual image
• value or brief description
• definition
The cards can be used in a variety of ways.
Suggestion 1
Pick one of the cards. Find all cards that depict the same key property.
Suggestion 2
Play a version of Memory. Turn all cards face down. Pick two cards. If they
depict the same key property, keep them. Otherwise, return them to the table
face down. (This could be played solitaire or with others.)
Suggestion 3
Use the cards to play any card game where matching is required.
Go Fish, for example, could be played. Each player is dealt a number of cards
(7). In turns, each player asks others for cards with the same key properties as
one he/she is holding in his/her own hand. When a player collects all four cards
representing a key property, the set is put down in front of them. The player with
the most sets in the end wins.
Other card games, or solitaire games requiring matching could be adapted.
Suggestion 4
Use the cards to pick random groupings for the class. Each student draws a
random card. Students with cards that match the same key property form a
group.
Notes:
The PDF of the cards were designed using the same size as Avery Business
Cards – style # 05371. A custom back is provided as the final page in this PDF
if you wish to run the sheet of cardstock through the printer twice.
The first ten properties are depicted in the four full pages (each property is in the
same relative position on each page) – the eleventh property is on the following
half page. (The custom back is the final page.)
Key Properties of the Sine Function
cycle
increasing
interval(s)
period
decreasing
interval(s)
maximum
value
domain
minimum
value
range
zeroes
amplitude
Key Properties of the Sine Function
Key Properties of the Sine Function
1 wave
0° to 90° ,
270° to 360°
360°
90° to 270°
1
{x | x !! R }
-1
{y | -1 ! y ! 1 }
0°, 180°, 360°
1
Key Properties of the Sine Function
the smallest part of
the graph, or the
smallest shape, that
repeats
the portion of the function
during which the y-values
keep getting higher while
moving forward along the
x-axis
the length of one
cycle
the portion of the function
during which the y-values
keep getting lower while
moving forward along the
x-axis
the y-value of a
highest point on the
graph
the set of all
possible x-values
for which the
function is defined
the y-value of a
lowest point on the
graph
the set of all
possible y-values
output by
the function
the x-values of
points on the
horizontal axis of
the curve
the maximum height
from the horizontal axis
through the middle of
the curve
Key Properties of the Sine Function
phase shift
0
the horizontal shift
left or right of a
function out of
standard position
Key Properties of the Sine Function - back of card - use Avery Business Card # 05371
Relations Cards
The card set contains:
o 14 “Graph” cards
o 11 “Context” cards
o 4 “Type of Relation” cards
o 2 “Function” cards
The answer key (last page) references the graph or context card numbers.
The cards can be used in a variety of ways.
Suggestion 1
Pick one of the “Type of Relation” cards (e.g., linear, quadratic, periodic, other) and one of the “Function”
cards, then find all the “Graph” cards that match.
Suggestion 2
Pick one of the “Type of Relation” cards (e.g., linear, quadratic, periodic, other) and one of the “Function”
cards, then find all the “Context” cards that match.
Suggestion 3
Pick one of the graph or context cards then select the matching “Type of Relation” card and the matching
“Function” card.
Suggestion 4
Create additional cards for the set.
Suggestion 5
Group the cards in different ways, and state your grouping criteria.
Graph 1
Graph 2
Graph 3
Graph 4
Graph 5
Graph 6
Graph 7
Graph 8
Graph 9
Graph 10
Graph 11
Graph 12
Graph 13
Graph14
Context 2
Context 1
An escalator runs non-stop.
A ferris wheel goes round and round.
Relationship:
Dependent Variable:
Relationship:
Dependent Variable:
distance between one stair tread and the
floor at the foot of the elevator
Independent Variable: elapsed time
distance between a person on the ferris
wheel and the ground
Independent Variable: time
Context 4
Context 3
Ocean tides cause the depth of the water
in the Bay of Fundy to vary.
Relationship:
Dependent Variable:
depth of water
Independent Variable: time
A battery operated pendulum swings back and forth.
Relationship:
Dependent Variable:
distance from the end of the pendulum to
its position in the central position
Independent Variable: time
Context 6
Context 5
Wendel prints this message over and over.
Relationship:
Dependent Variable:
Relationship:
Dependent Variable:
height of the pencil point above the line
Independent Variable: horizontal distance of the pencil point from
the margin
margin
The minute hand of a clock goes round and round.
distance from the end of the minute hand
to its position at 12 o’clock
Independent Variable: time
Context 8
Context 7
A kitchen sink, whose shape is a rectangular prism,
is filled with water many times per week.
Stock prices rise and fall.
Relationship:
Dependent Variable:
volume of water in the sink
Independent Variable: depth of water in the sink
Relationship:
Dependent Variable:
price of one share of a particular stock
Independent Variable: day of the year
Context 10
Context 9
An employee earns $25 per hour.
An elevator in a 10 story building
makes many several stops during the day.
Relationship:
Dependent Variable:
the number of the floor at which the
elevator doors open
Independent Variable: the number of stops the elevator has made
Context 11
A ball is dropped from a height of 5 metres
and bounces again and again until it stops.
Relationship:
Dependent Variable:
height of ball
Independent Variable: time
Relationship:
Dependent Variable:
income
Independent Variable: number of hours worked
Type of Relation
Type of Relation
linear
quadratic
Type of Relation
periodic
Type of Relation
other
function
not a
function
Answer Key – Graphs
No.
Linear
Quadratic
Periodic
Other
Function
1
No
(the graph is not a line)
No (the graph is not a
parabola)
Yes
No
Yes
2
No (the graph is not a line)
No (the graph is not a
parabola)
No (the graph does not have a horizontal
pattern that repeats regularly)
Yes
Yes
3
No (the graph is piece-wise
linear)
No (the graph is not a
parabola)
Yes
No
Yes
4
No (the graph is piece-wise
linear)
No (the graph is not a
parabola)
No (the graph does not have a horizontal
pattern that repeats regularly)
Yes
Yes
5
No (the graph is not a line)
Yes
No (the graph does not have a horizontal
pattern that repeats regularly)
No
Yes
6
Yes
No (the graph is not a
parabola)
No (the graph does not have a horizontal
pattern that repeats regularly)
No
Yes
7
No (the graph is not a line)
No (the graph is not a
parabola)
No (the graph does not have a horizontal
pattern that repeats regularly)
Yes
Yes
8
No (the graph is not a line)
No (the graph is not a
parabola)
Yes
No
Yes
9
No (the graph is not a line)
No (the graph is not a
parabola)
Yes
No
No (the graph does not pass
the vertical line test)
10
No (the graph is not a line)
No (the graph is not a
parabola)
Yes
No
Yes
11
No (the graph is not a line)
No (the graph is not a
parabola)
No (the graph does not have a horizontal
pattern that repeats regularly)
Yes
Yes
12
No (the graph is not a line)
No (the graph is not a
parabola)
Yes
No
Yes
13
No (the graph is not a line)
No (the graph is the inverse
of a quadratic function)
No (the graph does not have a horizontal
pattern that repeats regularly)
Yes
No (the graph does not pass
the vertical line test)
14
Yes
No (the graph is not a
parabola)
No (the graph does not have a horizontal
pattern that repeats regularly)
No
No (the graph does not pass
the vertical line test)
Answer Key – Contexts
No.
Linear
Quadratic
Periodic
Other
Function
1
No, since the distance cycles through
increases and decreases as the
escalator moves
No, since the distance cycles
through increases and decreases as
the escalator moves
Yes, since there is a pattern
that repeats regularly
No
Yes, since at any moment in time
there is only one distance value
2
No, since the distance cycles through
increases and decreases as the wheel
turns
No, since the distance cycles
through increases and decreases as
the wheel turns
Yes, since there is a pattern
that repeats regularly
No
Yes, since at any moment in time
there is only one distance value
3
No, since the depth cycles through
increases and decreases as the tide
rises and falls
No, since the depth cycles through
increases and decreases as the tide
rises and falls
Yes, since there is a pattern
that repeats regularly
No
Yes, since at any moment in time
there is only one depth value
4
No, since the distance cycles through
increases and decreases as the
pendulum swings
No, since the distance cycles
through increases and decreases as
the pendulum swings
Yes, since there is a pattern
that repeats regularly
No
Yes, since at any moment in time
there is only one distance value
5
No, since the distance cycles through
increases and decreases as the
minute hand rotates
No, since the distance cycles
through increases and decreases as
the minute hand rotates
Yes, since there is a pattern
that repeats regularly
No
Yes, since at any moment in time
there is only one distance value
6
No, since the height cycles through
increases and decreases
No, since the height cycles through
increases and decreases
Yes, since there is a pattern
that repeats regularly
No
No, since each character has
multiple heights above the line for
any given distance from the margin
7
Yes, since the rate of change of
volume with respect to depth of water
(for this rectangular prism) is constant
No, since it is linear
No, since there is no pattern
that repeats regularly
No
Yes, since for any depth value
there is only one volume value
8
No, since stock prices rise and fall
over time
No, since stock prices rise and fall
over time
No, since there is usually no
repeating pattern in the rise and
fall of stock prices over time
Yes
Yes, since at any time a stock has
only one price
9
No, since the number of the floor
where the elevator doors open goes up
and down from stop to stop
No, since the number of the floor
where the elevator doors open goes
up and down from stop to stop
No, since there is usually no
repeating pattern in the
elevator’s stops
Yes
Yes, since the elevator stops at
only one floor at a time
10
Yes, since the income rises at a
constant rate (i.e., $25 per hour)
No, since it is linear
No, since the income rises at a
constant rate (i.e., there is no
repeating pattern)
No
Yes, since for a specific number of
hours there is only one income
11
No, since the height rises and falls
several times until the ball stops
No, since the height rises and falls
several times until the ball stops
No, since the height to which
the ball bounces keeps
decreasing until the ball stops
Yes
Yes, since at any moment in time
there is only one ball height